BÄCKLUND TRANSFORMATION, LOCAL AND NONLOCAL CONSERVATION LAWS FOR NONLINEAR σ-MODELS ON SYMMETRIC COSET SPACES

2009 ◽  
pp. 295-301
Author(s):  
GUANGZHAO ZHOU ◽  
XINGCHANG SONG
Keyword(s):  
Conservation Laws ◽  
Bäcklund Transformation ◽  
Backlund Transformation ◽  
Coset Spaces ◽  
Nonlocal Conservation Laws

scholarly journals Nonlocal Conservation Laws of PDEs Possessing Differential Coverings

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1760
Author(s):  
Iosif Krasil’shchik
Keyword(s):  
Conservation Laws ◽  
Conservation Law ◽  
Gordon Equation ◽  
Bäcklund Transformation ◽  
General Nature ◽  
Backlund Transformation ◽  
Sine Gordon Equation ◽  
Modern Language ◽  
Nonlocal Conservation Laws

In his 1892 paper, L. Bianchi noticed, among other things, that quite simple transformations of the formulas that describe the Bäcklund transformation of the sine-Gordon equation lead to what is called a nonlocal conservation law in modern language. Using the techniques of differential coverings, we show that this observation is of a quite general nature. We describe the procedures to construct such conservation laws and present a number of illustrative examples.

Ablowitz–Kaup–Newell–Segur system, conservation laws and Bäcklund transformation of a variable-coefficient Korteweg–de Vries equation in plasma physics, fluid dynamics or atmospheric science

2020 ◽  
Vol 34 (25) ◽  
pp. 2050226 ◽  
Author(s):  
Yu-Qi Chen ◽  
Bo Tian ◽  
Qi-Xing Qu ◽  
He Li ◽  
Xue-Hui Zhao ◽  
...  
Keyword(s):  
Conservation Laws ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Bäcklund Transformation ◽  
Atmospheric Science ◽  
Backlund Transformation ◽  
Atmospheric Flow ◽  
Bilinear Bäcklund Transformation ◽  
De Vries ◽  
Nonlinearity Dispersion

For a variable-coefficient Korteweg–de Vries equation in a lake/sea, two-layer liquid, atmospheric flow, cylindrical plasma or interactionless plasma, in this paper, we derive the bilinear Bäcklund transformation, non-isospectral Ablowitz–Kaup–Newell–Segur system and infinite conservation laws for the wave amplitude under certain constraints among the external force, dissipation, nonlinearity, dispersion and perturbation.

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